The invention relates to a method for generating semi-empirical transfer functions. An existing design process known as the design for six sigma (DFSS) process focuses on meeting critical to quality (CTQ) parameters by controlling one or more key control parameters (KCP""s) and/or key noise parameters (KNP""s). In the DFSS process, the transfer functions can be represented as
Y=F(X1, X2, . . . X); or
CTQ=F(KCPs, KNPs).
The transfer functions may be developed using closed form analyses, numerical analyses, or experimentation. The numerical and experimental methods often use regression analysis and design of experiments. Closed form solutions are generally available for only relatively simple problems. These transfer functions are typically obtained in the DFSS process by brainstorming the relevant parameters and using regression analysis and design of experiments (DOE) to fit these parameters to the numerical analysis or experimental data. The resulting transfer functions are usually in a polynomial form. A drawback to this process is that polynomial transfer functions require relatively large DOE""s since the known physical relationships are not used. These resulting equations are cumbersome and provide little insight into physical relationships among the equation parameters.
An exemplary embodiment of the invention is directed to a method for determining a transfer function relating a critical to quality parameter to key parameters in a design for six sigma process. The method includes determining a dimensionless group containing a plurality of key parameters. The key parameters include key control parameters or key noise parameters that have an affect on the critical to quality parameter. A transfer function relating the dimensionless group to the critical to quality parameter is then generated.